Coyle revealed Kone was in talks with Everton today.
He told BBC Radio 5 Live: "I'm led to believe through his representative that Everton is the club he wants to join,'
"It's not rocket science to say that Arouna Kone will probably leave at some point this week. There have been a number of offers in for him.
"There is no problem, he goes with our blessing because I need players who need to be at Wigan. If his heart's elsewhere then he's no good to me."